One year, 41 million digits: How he found the largest known prime number
Luke Durant was folding his laundry right into his suitcase ahead of a trip back home to Alabama when he decided to check his computer and see if he had made history.
He figured that, like every other time over the past year of fixing computer scripts, he probably hadn’t. That night, Oct. 12, he was wrong.
Durant had discovered the world’s new largest prime number. He quickly told his partner that this was going to complicate the trip, then got to work double-checking his computer’s result.
The number he found, given the unstimulating name M136279841, is one of those figures so outlandishly large that it doesn’t sound real. It has 41,024,320 decimal digits. If someone read off the entire number and each digit took one second to say, they would need 475 days to finish. Apologies in advance if this hurts your brain, but: The number is two to the 136,279,841st power minus one.
The discovery was the result of almost exactly one year of work and about $2 million of Durant’s own money.
The 36-year-old programmer retired from chipmaker Nvidia in 2021. He had joined a decade earlier at the start of a technology boom that would see the company surpass Microsoft in June 2024 as the world’s most profitable company with a market capitalization of $3.3 trillion. Nvidia builds the graphics processing units, or GPUs, and software that power the artificial intelligence algorithms behind the chatbots and image generators sweeping the internet.
Durant, a graduate of the California Institute of Technology, found the new prime number using only publicly available unused cloud storage space. Durant, who made his money off the boom, said he put his time and money into the project to show people that they aren’t helpless to technology giants and that we can figure out massive problems if we work together.
“Individuals today are dramatically more capable than any point in history,” he said. “The scale of computing available in the cloud, it’s nearly unfathomable. I was able to find this number that’s astonishingly large … but I was able to do it just by using big tech’s leftovers. So it’s trying to [highlight the fact that] we have these incredible systems, so let’s figure out how to best use them.”
The prime number Durant discovered serves no real purpose for society. This isn’t the key to curing a disease or proving some universal scientific theory.
“It’s entertainment for math nerds,” said George Woltman, co-founder of the Great Internet Mersenne Prime Search.
Woltman’s organization, which announced Durant’s discovery on Monday, provides software and support for people on this numerical quest. Woltman and Durant said they are seeking Mersenne primes, a type of prime number named after the French monk Marin Mersenne, who studied them in the 17th century.
Woltman, 67, said he has been interested in primes and recreational math since he was a kid. While other children were playing outside, he and his programmer father were writing a prime number computer code.
A former computer programmer himself, Woltman said the search for new primes has been a retirement hobby.
“It’s a good way to pass some time,” he said, noting that it offers literally infinite enjoyment.
Woltman said about 3,00o to 5,000 volunteers have downloaded a piece of software that tasks unused space on their computers to crunch these numbers in the background.
But it is getting harder to find numerical needles in a haystack - Woltman’s announcement said the last one was found in 2018 and is 16 million digits shorter than Durant’s discovery, which is the 52nd Mersenne prime.
For the past 28 years, Woltman’s group has helped find 18 Mersenne primes. All that work was done on CPUs, or central processing units, which are the hearts of modern personal computers. Durant did something different. He used the GPUs, the technology he had a hand in developing at Nvidia.
A typical CPU would take a week or two to test a number to see whether it is prime, Woltman said. It takes GPUs about a day or two.
This technological leap is a key to why the consumer advocacy group Electronic Frontier Foundation began offering rewards for finding such humongous numbers, said Jacob Hoffman-Andrews, a senior staff technologist at EFF.
Some of the rewards have been claimed, but others remain open, including a $250,000 prize for the first person to find a billion-digit prime.
Hoffman-Andrews said the group started offering rewards March 30, 1999 - almost two years before Wikipedia was launched. They wanted to develop ways to work across the internet, which, he said, was still new and not the given that it is today.
“Proving the potential for computers to coordinate and people cooperating on the internet is something we no longer need to prove, but this prize was created with a long horizon,” he said.
Hoffman-Andrews said it is the journey, not the destination, that is worth celebrating since the prime numbers are useless.
He compared Mersenne primes to test cars: “It won’t help you get the milk home any faster, but it’s fun and impressive and occasionally provides insights into how to build faster vehicles.”
Durant’s use of GPUs, starting in October 2023, quickly made him the most prolific prime pioneer using software from Woltman’s group.
He used servers in 17 countries across 24 data centers and on two cloud providers to find the number, Durant said. But the spirit of his discovery is distinctly human despite all of it happening on a computer.
Durant went to public school in Alabama, which consistently ranks as offering some of the nation’s lowest-quality public education. He said that in his circles, the South doesn’t get recognition for its scientific or technical experts. So he’s donating the $3,000 prize money from Woltman’s group to the Alabama School of Math and Science, the public boarding school he attended before Caltech.
Durant said he also spent the time and money on finding a prime number to show that GPUs can be used for more than AI. He said he wants the technology to be used for research and discovery - for prime numbers and beyond.
“An AI isn’t going to be able to find the next prime number,” he said. “And, of course, I may have to end up eating those words someday.”
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